To expand on "stalls" a bit, they aren't a magic thing that happens that makes planes fall. Simply put, they happen when a wing is angled up too "steeply" for the speed it is going. Once it gets past a certain angle, the air can't flow smoothly around it, so it stops providing any lift (known as separation).

So as a pilot, the two things you can control in order to make more lift are the airspeed and the wing angle. The airspeed is limited by the thrust of the engine (at least in level flight), and the wing angle is limited by the stall angle. In this video, the pilot is likely at maximum thrust, so the only thing he can do to increase his lift is try and pull the nose up, which leads to a stalled condition (rather abrupt decrease in lift). If his engine was performing correctly, the fact that he couldn't maintain a climb at that or any lower angle meant the airplane was likely overweight for the conditions.